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This publication represents the paintings of most sensible scientists within the box of clever keep an eye on and its purposes, prognostics, diagnostics, established upkeep and unmanned structures. The paintings offers an method of fixing engineering difficulties with regards to production, automation, and particularly unmanned structures and describes contemporary advances within the disciplines pointed out above. the most target of the publication is to illustrate how options and concepts from different disciplines are merged inside of a standard framework utilized to the answer of complicated problems.
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Extra resources for Applications of Intelligent Control to Engineering Systems: In Honour of Dr. G. J. Vachtsevanos
Veaux, J. Schweinsberg and J. Ungar, Prediction intervals for neural networks via nonlinear regression, Technometrics 40(4), 273–282, November 1998. 28. P. Wang and G. Vachtsevanos, Fault prognostics using dynamic wavelet neural networks, Artificial Intelligence for Engineering Design, Analysis and Manufacturing 15(4), 349–365, September 2001. 29. W. Weibull, A statistical distribution function of wide applicability, Journal of Applied Mechanics 18, 293, 1951. 30. S. A. Gershenfeld, Time Series Prediction: Forecasting the Future and Understanding the Past, Addison-Wesley, MA, 1993.
5) Kopt (x) = ⎩ 0 otherwise, where cnx is the volume of the unit sphere in Rnx . Furthermore, if the density is Gaussian with unit covariance matrix, the optimal bandwidth is given by hopt = A · N −1/nx +4 , √ A = 8cn−1 · (nx + 4) · 2 π x nx 1/nx +4 . 6) The Epanechnikov kernel is particularly recommended in the special case of equally weighted samples , and thus it is well suited for uncertainty representation in long 2 Particle Filtering Applied to Prognostics 27 term predictions where no future measurements are available for a weight update procedure.
Accuracy of long-term predictions is directly related to the estimates of xt and the model hyper-parameters that affect E[xt | xt −1 ]. Precision in long-term predictions, on the other hand, is directly related to the hyper-parameters that describe the variance of the noise structures considered in the state equation. 3, where the performance of the algorithm is evaluated in terms of the short-term prediction error (which depends on the PF-based pdf estimate). Whenever the performance criteria for the short-term prediction error are not met, an outer correction loop directly modifies both model parameters and hyper-parameters.